44. How many farthings in 4 pence? In 2700 pence? .1. 10816 farthings.

45. How many pence in 8 farthings? In 6200 farthings? A. 1552 pence.

PRACTICAL APPLICATION OF REDUCTION, Involving the Rule, with Miscellaneous Examples.

1. At 20 cents a quart, what will 2 gallons of rum cost? What will 4 gallons? What will 5 gallons?

2. At $60 a hogshead, what will 2 pipes of wine come to? What will 4? What will 6?

3. How many minutes in 2 hours? In 4? In 6?

4. How many weeks in 14 days? In 21? In 49 ?

Q. What are such questions as these in?

A. Reduction.

Q. What, then, is the changing numbers from one denomination to another called?

A. Reduction.

Q. In 2 bushels of corn, how many pecks!

Q. Are 8 pecks of corn as much as 2 bushels ?

Q. Is the value altered, then?

Q. Do you multiply or divide, to find how many furlongs there are in 2 miles?

Q. When, then, the reduction is performed by multiplication, what is it called?

A. Reduction Descending.

Q. Do you multiply or divide to find how many gallons there are in 8 quarts?

Q. When, then, the reduction is performed by division, what is it called?

A. Reduction Ascending.

Q. From the preceding remarks, how many kinds of reduction do there appear to be? and what are they?

A. Two-Reduction Ascending and Descend

ing.

RULE.

Q. What do you multiply 2 'arlongs by, to bring them into rods? Q. As a general rule, then, what do you multiply furlongs by? A. By what makes a furlong.

Q. What do you multiply days, bushels, &c. by?

4. Bushels by what makes a bushel, days by what makes a day, &c.

Q. What do you divide by to bring 8 gills into pints?

Q. As a general rule, then, what must you divide gills, minutes, quarters, &c. by?

A. Gills by gills, minutes by minutes, quarters by quarters, &c.

Q. Why do you divide thus ?

A. Because 4 gills are equal to 1 pint, 60 minutes to 1 hour, &c

Q. What do you multiply pounds (money) by?

A. Shillings.

Q. What do you multiply by, to bring 25 pounds into farthings? A. By 20, 12, and 4.

Q. How do you bring 40 cwt. into_tons? I cwt. into drams? 1 ton into drams? Drams into tons? Drams into cwt. 1 lb. into grains? Grains into pounds? Ells Flemish into nails? Nails into ells Flemish Quarters into ells English? Ells English into quarters ? 5 bushels into pints? 200 pints into bushels? 360 degrees into inches? Feet into furlongs? 5 weeks into seconds? Seconds into weeks? Years into seconds? Seconds into years? How do you tell what? tun of wine will cost, at 6 cents a gill?

Exercises for the Slate.

46. At 6 cents a pound, what will 2 qrs. 8 lbs. of sugar cost?

OPERATION.

qrs. lbs.

2 8 28

56 lbs.

8 lbs.

64 lbs.

6 cts. $3,84 Ans.

Q. Why do you multiply the 2 qrs. by 28 lbs.?

A. Because, since it takes 28 pounds to make 1 qr., there will of course be 28 times as many pounds as quarters; that is, 28 times the quarters.

Q. What do you do with the 8 lbs.?
A. 1 add it to 56 lbs., making 64 lbs.
Q. Why do you multiply the 64 lbs. by
6 cents?

A. Because every pound of sugar cost 6 cents; that is, 6 times the pounds.

Proof of the foregoing Example.

47. How many quarters of sugar can you buy for 384 cents,

at 6 cents a pound?

OPERATION.

6) 384

28) 64 ( 2 qrs. 56

8 lbs. Ans. 2 qrs. 8 lbs.

Q. Why do you divide 384 cents by 6 cents?

A. Because, since there are 6 times as many cents as pounds, as often as 6 is contained in 384, so many pounds there will be.

Q. Why do you divide 64 pounds by 28 pounds?

A. Because every 28 pounds make 1 quarter.

Q. What, then, appears to be the method of proof?

A. Reverse the operation; that is, make the divisors in the operation the multipliers in the proof, and the multipliers the divisors.

In examples like the following, where more than one operation in a simple rule is employed in their solution, their entire work is inserted in the Key, by means of signs, indicating the exact process of each, with all their intermediate results, to the final one, or answer. Besides, when the question is at all intricate, the reason for every step in the required operation is fully shown.

More Exercises for the Slate.

48. At 5 cents a gill, what will 8 pints of rum cost? A. $1,60. 49. How many gills in 20 pints? In 40 pints? A. 240 gills. 50. How many pints in 80 gills? In 120? A. 50 pints. 51. A merchant sold 5 hhds. of brandy, at 3 dollars a gallon, how much did it amount to? A. $945.

52. How many hogsheads in 126 gallons? In 945? 2. 17. 53. At 6 cents a quart, what will I hhd. of molasses come to ? A. $15,12.

54. How many quarts are there in 3 hhds.? In 100? A. 25956.

55. How many hogsheads are there in 756 qts.? In 252 qts.? A. 4.

56. Sold 1 tun of wine, at 5 cents a gill; what did I get for it? A. $403,20.

57. How many gills in 10 tuns? A. 80640.

58. At 8 cents a pound, what will 3 cwt. 2 qrs. of raisins cost? A. $31,36.

59. How many pounds in 15 cwt. 1 qr.? A. 1708.

60. At 8 pence a peck, how many pence will 3 bushels of salt cost? A. 96.

61. How many pence are there in 20 shillings? A. 240.

62. How many pence in 5 £.? In 10? A. 3600.

63. How many pounds in 480 d.? In 1440 d.? A. 8. 64. How many farthings in 4 £.? A. 3840.

65. At 6 pence per lb., what will two qrs. of rice cost? A. 336 pence.

66. How many qrs. of rice, at 6 pence per lb., may be bought for 336 pence? A. 2 qrs.

67. At 6 cents a gill, what will 1 tun of wine cost? A. $483,84.

63. How many tuns of wine, at 6 cents a gill, may be bought for $483,84. A. 1 tun.

69. At 9 pence per quart, what will 16 gals. 2 qts. of molasses come to in pence? A. 594 pence.

70. How many gallons of molasses, at 9 pence per quart, may be bought for 594 pence? A. 16 gals. 2 qts.

71. What is the value of a silver cup, weighing 10 oz. 5 pwts. 18 grs., at 5 mills per grain? A. $24,69.

72. At 5 mills per grain, what will be the weight of a silver cup that $24,69 will purchase? A. 10 oz. 5 pwts. 18 grs.

73. At 12 cents a pound, what cost 5 cwt. 2 qrs. 18 lbs. of sugar? A. $76,08 cts.

74. How many hundred weight of sugar, at 12 cents per lb., may be bought for $76,08? A. 5 cwt. 2 qrs. 18 lbs.

75. At 9 pence an hour, what will 2 yrs. 6 mo. 3 weeks, 6 da 12 h. labor come to in pence? A. 187380.

76. How many years' work, at 9 pence per hour, may be obtained for 187380 pence? A. 2 yrs. 6 mo. 3 weeks, 6 da

12 h.

77. At 20 cents a nail, what is the price of 4 yds. of cloth? A. $12,80.

78. At 320 cents a yard, what will 64 nails of cloth cost? A. $12,80.

79. At 1 £. 2 s. 64 d. per yard, what will 20 yds. of broadcloth cost in farthings? A. 21640.

80. At 6 cents a pint, what will 20 bu. 0 pks. 3 qts. 1 pt. of flax-seed cost? A. $77,22.

81. How many shillings, at 2 farthings a gill, will 5 T. 1 p. 1 hhd. 2 gals. 2 qts. 1 pt. 3 gills, cost? A. 1935 s. 7 d. 2 qrs. 82. At 2 shillings a quarter, how many dollars will 8 yds. 1 qr. of broadcloth cost? A. 11.

63. At 2 pence a gill, how many dollars will buy 50 gals. 2 qts. 1 pt. 2 gills of ale? A. $45,055.

84. In 3600 dollars, how many farthings? A. 1036800. 85. In 1036800 farthings, how many dollars? A. 3600. 86. In 25 guineas, of 28 s. each, how many pence? A. 8400. 87. In 8400 pence, how many guineas? A. 25.

88. In 15 lbs. how many ounces, drams, scruples, and grain« › A. 180 ounces, 1440 drams, 4320 scruples, 86400 grains.

89. In 86400 grains, how many scruples, drams, and ounces A. 4320 scruples, 1440 drams, 180 ounces.

90. In 256 miles, 30 rods, how many rods? A. 81950.

91. In 81950 rods, how many miles? A. 256 m. 30 rods. 92. In 15 lea. 1 m. 6 fur. 28 rods, 4 yds. how many barlev corns? A. 8903304.

93. In 8903304 barley corns, how many leagues? A. 15 lea 1 m. 6 fur. 28 rods, 4 yds.

94. In 360 ells English, 4 qrs. 2 n. how many nails? A. 1804 qrs. 7218 na.

95. In 7218 na. how many ells English? A. 360 E. E. 4 qrs.

2 na.

96. In 3000 E. Flemish, how many nails? A. 36000.
97. In 36000 nails, how many E. Flemish? A. 2009.
98. In 500 acres, how many roods? A. 2000.
99. In 2000 roods, how many acres?

A. 500.

100. In 15 tons of hewn timber, how many solid inches? .9. 1296000.

101. In 1236000 solid inches of hewn timber, how many tons? A 15.

102. In 20 cords of wood, how many solid inches? A. 4423680.

103. In 4423680 solid inches, how many cords of wood? A. 20.

104. In 500 bushels, 3 pecks, 7 qts. 1 pt. how many pints?

A. 32063.

105. In 32063 pints, how many bushels? A. 500 bu. 3 pks. 7 qts. 1 pt.

4. 20.

106. In 20 tuns of wine, how many gills? A. 161280. 107. In 161280 gills of wine, how many tuns? 108. In 360 years, 300 days. 20 hours, 50 minutes, and 37 seconds, how many seconds? A. 11386731037.

109. In 11386731037 seconds, how many years? A. 360 yrs. 300 days, 20 hours, 50 minutes, and 37 seconds.

110. In 8 signs of the Zodiac, how many seconds? A. 864000.

111. In 20 purses, each containing 21 guineas, how many shillings, pence, and farthings? A. 11760 s. 141120 d. 564480) far.

112. In 5 ingots of silver, each 5 lbs. 6 oz. 20 grs., how many grains? A. 158500.

113. In 239139 grains, how many ingots, each 6 lbs. 11 oz. 15 grs.? A. 6.

114. A lady sent a tankard to a silversmith, that weighed 5 lbs. 3 oz. and ordered it to be made into spoons, each to weigh 2 oz. 2 pwts; how many spoons did it make? A. 30.

115. A goldsmith, having 15 ingots of silver, each weighing 2 lbs. 7 oz. 3 pwts., which he wishes to make into bowls of 2 lbs.